The Metro Board will begin hearings throughout the metropolitan area next week on fare increases for both the bus and subway systems. Fares are expected to increase for Northern Virginia passengers on June 29, although it is difficult to say by how much because of a highly-complex set of fare proposals made by the local governments of Northern Virginia.

There are three different sets of proposed new (and higher) bus fares, and two plans for new (and higher) subway fares. When the two are combined for the kind of typical bus and subway trip many Virginians take to work every day, the possibilities boggle the mind.

Depending on where one lives and which proposal is adopted, fares for one day's round trip could increase by as little as five cents or as much as 40 cents.

Metro, which follows local government instructions in fare matters, has scheduled four public hearings, all of which will begin at 7:30 p.m., as follows:

Tuesday, March 25 -- George Mason Junior-Senior High School, Leesburg Pike and Haycock Road, Falls Church.

Thursday, March 27 -- Alexandria City Council chambers, 125 N. Royal St., Alexandria.

Wednesday, April 2 -- Arlington County Courthouse, 1400 N. Courthouse Rd., Arlington.

Tuesday, April 8 -- Lee High School, 6540 Franconia Rd., Springfield.

Metro is projecting a record $276 million operating budget for the fiscal year beginning July 1, a 44 percent increase over the preceding year. Two-thirds of that cost is attributable to the bus operation, which helps explain why Fairfax County, Arlington and Alexandria all are discussing the idea of running their own bus systems.

In the meantime, however, the fare increases have been proposed to see if the Northern Virginia share of the Metro deficit -- estimated at $35.2 million -- can be trimmed with help from the rider. Subway Fares

Two subway fare schedules are up for discussion. One would raise rush-hour fares by about 11 percent for all trips; the other would raise rush-hour fares approximately 22 percent for all trips. Rush-hour fares are changed weekdays between 6 a.m. and 9:30 a.m. and between 3 p.m. and 6:30 p.m.

Under the 11-percent solution, the basic rush-hour fare would increase from 45 cents to 50 cents. An additional 10.5 cents would be charged for each additional mile.

A trip from the Pentagon to Metro Center, which now costs 50 cents, would increase to 55 cents. A ride from Ballston to L'Enfant Plaza, now 70 cents, would go to 80 cents.

Under the 22-percent suggestion, the minimum rush-hour fare for a three-mile trip would be 55 cents, with 11.5 cents charged for each additional mile. The fare from the Pentagon to Metro Center would go from 50 cents to 60 cents; the trip from Balston to L'Enfant Plaza would increase from 70 cents to 85 cents.

There would be no change in the present 50-cent "off-peak" fare for all trips, regardless of length, which is charged at mid-day, at night and on weekends and holidays.

Fares for the elderly and handicapped would continue to be half the regular rush-hour fare, up to a maximum of 50 cents per trip. Bus Fares

The Northern Virginia governments have proposed three different bus fare schedules. The rush-hour schedules are detailed in the accompanying chart and include a variety of proposed zone-charge changes. The 30-cent surcharge to Reston commuters would be retained, regardless of which fare schedule is adopted.

There are also variations in the nonrush-hour fare proposals. Under one alternative, the rush hour fare would be charged at all times. Under a second alternative, the off-peak fare would be increased from 50 cents to 60 cents and the Potomac River off peak zone charge would rise from 30 to 60 cents.

Under a third plan, the off-peak base fare would increase from 50 to 55 cents, and the river-crossing charge would go from 30 cents to 45 cents.

The 30-cents surcharge on Reston routes would be retained.

Bus fares for elderly and handicapped persons would be increased to half the rush-hour fare at all times. The present policy is to charge half the off-peak at all times. Rail-Bus Transfers

As at present, there will be no transfer credit for switching from bus to subway.

Riders can transfer free from subway to bus within the District of Columbia.

Under one Virginia alternative, transfer credit from rail to bus would be eliminated and full bus and subway fares would have to be paid every time. Under another alternative, the transfer would be worth 75 cents, but zone charges would be assessed. Under the third alternative, the transfer plus 30 cents plus zone charges would buy the rider a seat on the bus.

The charts list sample round-trip fares for combined bus and subway fares for all alternatives, from points in Virginia to Metro Center and back. Passes

Virginia is considering three passes. The cost and value of each would depend on the bus and subway fare schedules ultimately chosen. Regardless of final price, Virginia is planning a base pass -- good for unlimited travel within Virginia -- a two-zone pass and a three-zone pass. The pass may or may not have value on the subway, depending on the fare schedule chosen.